For a timepiece to have the best possible isochronism, it is necessary to act on the construction parameters of the balance and the balance-spring, and on the choice of materials, in order to improve the intrinsic performance of the regulating device and to compensate for or reduce variations of rate due to variations in external conditions, such as the temperature or magnetic field.
As far as the balance-spring is concerned, the shaping of the outer curve for fastening it directly or indirectly to the balance-cock, the shaping of the inner curve for fastening it to the balance staff to allow concentric development of the coils, and the choice of materials play a determining part as regards isochronism.
The invention concerns more specifically both the shaping of the inner curve and the choice of materials for making the inner curve and the set of coils. In order to attain this object, a well-known solution is to choose a non-magnetic material with a low thermal expansion coefficient and applying the “point of attachment” rule to shape the inner curve of a balance-spring along a particular contour, and particularly along the Grossmann curve. In order to make such a curve at the inner end of a balance-spring, all of whose coils have previously been formed by the known winding technique, it is necessary to rely on a highly qualified labour force, such that this solution is reserved for high precision, top of the range timepieces and for limited series but is not applicable to large scale manufacture. Given the technological development, in order to give the balance-spring the optimum shape, one could envisage making the entire balance-spring by photolithography and galvanic growth. However, in the state of the art, there exists no metal or alloy that is satisfactory both for its electro-plating shapeability and for its properties of elasticity and thermal expansion coefficient.